A seismic survey represents an attempt to image or map the subsurface of the earth by sending sound energy down into the ground and recording the “echoes” that return from the rock layers below. The source of the down-going sound energy might come, for example, from explosions or seismic vibrators on land, or air guns in marine environments. During a seismic survey, the energy source is placed at various locations near the surface of the earth above a geologic structure of interest. Each time the source is activated, it generates a seismic signal that travels downward through the earth, is reflected, and, upon its return, is recorded at a great many locations on the surface. Multiple source/recording combinations are then combined to create a near continuous profile of the subsurface that can extend for many miles. In a two-dimensional (2D) seismic survey, the recording locations are generally laid out along a single line, whereas in a three dimensional (3D) survey the recording locations are distributed across the surface in a grid pattern. In simplest terms, a 2D seismic line can be thought of as giving a cross sectional picture (vertical slice) of the earth layers as they exist directly beneath the recording locations. A 3D survey produces a data “cube” or volume that is, at least conceptually, a 3D picture of the subsurface that lies beneath the survey area. In reality, though, both 2D and 3D surveys interrogate some volume of earth lying beneath the area covered by the survey.
A seismic survey is composed of a very large number of individual seismic recordings or traces. In a typical 2D survey, there will usually be several tens of thousands of traces, whereas in a 3D survey the number of individual traces may run into the multiple millions of traces. Chapter 1, pages 9-89, of Seismic Data Processing by Ozdogan Yilmaz, Society of Exploration Geophysicists, 1987, contains general information relating to conventional 2D processing and that disclosure is incorporated herein by reference. General background information pertaining to 3D data acquisition and processing may be found in Chapter 6, pages 384-427, of Yilmaz, the disclosure of which is also incorporated herein by reference.
A seismic trace is a digital recording of the acoustic energy reflecting from inhomogeneities or discontinuities in the subsurface, a partial reflection occurring each time there is a change in the elastic properties of the subsurface materials. The digital samples are usually acquired at 0.002 second (2 millisecond or “ms”) intervals, although 4 millisecond and 1 millisecond sampling intervals are also common. Each discrete sample in a conventional digital seismic trace is associated with a travel time, and in the case of reflected energy, a two-way travel time from the source to the reflector and back to the surface again, assuming, of course, that the source and receiver are both located on the surface. Many variations of the conventional source-receiver arrangement are used in practice, e.g. VSP (vertical seismic profiles) surveys, ocean bottom surveys, etc. Further, the surface location of every trace in a seismic survey is carefully tracked and is generally made a part of the trace itself (as part of the trace header information). This allows the seismic information contained within the traces to be later correlated with specific surface and subsurface locations, thereby providing a means for posting and contouring seismic data—and attributes extracted therefrom—on a map (i.e., “mapping”).
The data in a 3D survey are amenable to viewing in a number of different ways. First, horizontal “constant time slices” may be taken extracted from a stacked or unstacked seismic volume by collecting all of the digital samples that occur at the same travel time. This operation results in a horizontal 2D plane of seismic data. By animating a series of 2D planes it is possible for the interpreter to pan through the volume, giving the impression that successive layers are being stripped away so that the information that lies underneath may be observed. Similarly, a vertical plane of seismic data may be taken at an arbitrary azimuth through the volume by collecting and displaying the seismic traces that lie along a particular line. This operation, in effect, extracts an individual 2D seismic line from within the 3D data volume. It should also be noted that a 3D dataset can be thought of as being made up of a 5D data set that has been reduced in dimensionality by stacking it into a 3D image. The dimensions are typically time (or depth “z”), “x” (e.g., North-South), “y” (e.g., East-West), source-receiver offset in the x direction, and source-receiver offset in the y direction. While the examples here may focus on the 2D and 3D cases, the extension of the process to four, five, or six dimensions is straightforward.
Seismic data that have been properly acquired and processed can provide a wealth of information to the explorationist, one of the individuals within an oil company whose job it is to locate potential drilling sites. For example, a seismic profile gives the explorationist a broad view of the subsurface structure of the rock layers and often reveals important features associated with the entrapment and storage of hydrocarbons such as faults, folds, anticlines, unconformities, and sub-surface salt domes and reefs, among many others. During the computer processing of seismic data, estimates of subsurface rock velocities are routinely generated and near surface inhomogeneities are detected and displayed. In some cases, seismic data can be used to directly estimate rock porosity, water saturation, and hydrocarbon content. Less obviously, seismic waveform attributes such as phase, peak amplitude, peak-to-trough ratio, and a host of others, can often be empirically correlated with known hydrocarbon occurrences and that correlation applied to seismic data collected over new exploration targets.
One well known problem with seismic data, though, is that in many cases it is impractical or impossible to acquire data in some limited parts of a planned survey, i.e., there may be skips, gaps, or localized regions of overwhelming noise that result in gaps in the seismic coverage and/or fold. Those of ordinary skill in the art will be very familiar with the sorts of field problems that can result in low fold data including regions of localized noise (due, e.g., to the presence of a highway, electrical lines/generators, construction), regions where seismometers cannot be placed (e.g., because of surface water such as lakes), inability to permit a parcel of land, etc.
Additionally, in some cases it is impractical or impossible to acquire regularly spaced traces in some parts of the survey area. That is, rather than obtaining uniformly and equally spaced shot/receiver spacings that are collected exactly as they were planned in the office of the explorationist, the actual collection of data in the field may result in irregular spacing of shots, receivers or both. This results in a wavefield that is sampled irregularly. This irregular sampling can cause artifacts in seismic images that were produced by using processing algorithms that presuppose a regularly sampled wavefield.
Many seismic processing algorithms (e.g., migration) work best when the input data are regularly sampled spatially and are of full fold, i.e., where the data do not have skips, gaps, etc. To that end, a variety of interpolation schemes have been devised that are designed to use existing trace data to estimate the signal content of traces that are missing or corrupted. Among those that have been utilized with some success are a class of estimators known as “Projection Onto Convex Sets” (“POCS”, hereinafter) interpolation algorithms.
However, as useful as POCS has proven to be, its application in practice has added a significant amount of time and cost to the processing of the seismic data because of the computer resources that are required to calculate it. That is, this method of interpolation is computationally intensive and, although many datasets that could benefit from an application of this technique, its application has occasionally been avoided to save time and computer resources in the processing of the data.
Heretofore, as is well known in the seismic processing and seismic interpretation arts, there has been a need for a method of estimating seismic signal values in regions of missing coverage that produced a good interpolation and that can be applied to large seismic datasets. Additionally, there has been a need for an interpolation method that is capable of taking advantage of the higher dimensionality of seismic data, something which has not been done heretofore, as most prior art interpolation methods have tended to focus on only two dimensions of the seismic data. Accordingly, it should now be recognized, as was recognized by the present inventor, that there exists, and has existed for some time, a very real need for a method of seismic data processing that would address and solve the above-described problems.
Before proceeding to a description of the present invention, however, it should be noted and remembered that the description of the invention which follows, together with the accompanying drawings, should not be construed as limiting the invention to the examples (or preferred embodiments) shown and described. This is so because those skilled in the art to which the invention pertains will be able to devise other forms of this invention within the ambit of the appended claims.